Traveling wave solutions of advection-diffusion equations with nonlinear diffusion

L. Monsaingeon, A. Novikov, J. M. Roquejoffre

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds cε]C*,+∞[, where C*>0 is explicitly computed but may not be optimal. We also prove that a free boundary hypersurface separates a region where u=0 and a region where u>0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u>0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.

Original languageEnglish (US)
Pages (from-to)705-735
Number of pages31
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume30
Issue number4
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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